Ninja_Bait: Ether has already answered this question in an earlier post... I think the issue is the notion of supplying a larger torque indefinitely. Perhaps it will help to say it another way?
The system will accelerate to a speed where you are no longer able to supply torque greater than tau_k. Physical systems are power limited and power = torque * angular rate. The system will accelerate to the limits of your power supply or motor torque vs speed curve (which ever comes first). At that point the torque supplied by the motor will again be tau_k and you will have constant speeds.
If you could somehow supply a constant torque independent of speed, the system as modeled would properly accelerate forever. Other effects would eventually dominate and the model would become invalid so this wouldn't actually happen, but you would still want to patent that motor and power supply!
